JPH11230833A - Method and apparatus for measuring phase distribution - Google Patents

Abstract

(57) [Problem] To provide a method and an apparatus capable of measuring a phase distribution of a test object three-dimensionally in a short time. SOLUTION: Coherent light from the same light source 1 is referred to as a
And a test wave b passing through the test object A, in which two wavefronts are overlapped to form an interference fringe by overlapping both wavefronts, the reflection mirror 7 and / or 9 is tilted by an angle γ. At the same time, these reflecting mirrors were fixed. In addition, the Fourier transform method is used to analyze the interference fringes to achieve high speed.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a technique for three-dimensionally measuring a phase distribution in a test object by analyzing interference fringes.

[0002]

2. Description of the Related Art In recent years, plastics have been increasingly used as materials for optical lenses used in optical devices such as laser printers and cameras. Compared to a glass polished lens, a plastic molded lens has advantages in that it is superior in cost reduction and manufacturability of an aspherical lens and is inexpensive.

[0003] On the other hand, however, the refractive index distribution is unstable in production as compared with a glass lens, and non-uniformity may occur inside the lens. Non-uniformity inside the lens has a great effect on optical characteristics, leading to deterioration of image quality and blurring. Therefore, it is necessary to measure the refractive index distribution inside the lens with high accuracy and evaluate the homogeneity of the optical lens.

Accordingly, the applicant of the present invention has disclosed in
In No. 22210, a test object immersed in a test solution is rotated about an axis orthogonal to the optical axis, and a reference wave based on coherent light from the same light source and a test wave transmitted through the test object These two light beams are superimposed at each of a plurality of rotation angle positions to form an interference fringe, the amount of transmitted wavefront is measured from these interference fringes by the phase shift method, and these are re-analyzed by CT analysis. A method and an apparatus for determining the phase distribution of the test object, such as the refractive index, have been proposed.

A specific description will be given with reference to FIG. The device shown in the figure has a basic configuration of a Mahachender type interferometer.
A light source 1 for emitting laser light as coherent light, a polarizer 2, a mirror 3, a beam expander 4, a beam splitter 5 for splitting a light beam, two reflecting mirrors 7 and 9, and a beam for superimposing a light beam Splitter 11 and imaging lens 13
And an interference fringe detector 15 composed of a CCD or the like, and an arithmetic processing unit 17 composed of a high-speed image processing device, a microcomputer or the like. Of the above configuration, the interferometer is configured by the light source 1 to the interference fringe detector 15.

A laser beam emitted from a light source 1 is a polarizer 2
, Is reflected by the mirror 3 and is incident on the beam expander 4, whereby the beam diameter is enlarged, and the reference wave a is bent at a right angle by the beam splitter 5.
, And is bent at a right angle by the mirror 9, and is divided into a test wave b that passes through a phase object as the test object A. The reference wave a and the test wave b are set to be approximately 1: 1.

The reflection mirror 7 is supported by an electric-displacement conversion element 19 such as a piezo element, so that the optical path length of the reference wave a can be changed on the order of a wavelength or less in order to perform interference fringe analysis by a phase shift method. Are located.

The reference wave a is reflected by the reflection mirror 7 and reaches the beam splitter 11, while the other test wave b is the test object A
And reaches the beam splitter 11 and overlaps with the reference wave a, but is adjusted by the electric-displacement conversion element 19 so that the optical path length between the reference wave a and the test wave b has a phase difference of nπ / 2. Is done.

The reference wave a and the test wave b are superimposed and split from the beam splitter 11 into two light beams. One light beam travels straight and enters the imaging lens 13, and the interference fringe detector 1
An interference fringe is imaged on the imaging surface of No. 5. As the interference fringe detector 15, a linear CCD or an array sensor is used. The light beam that is bent at right angles by the beam splitter 11 enters another imaging lens 23 and forms an interference fringe on a monitor 25.

The refractive index of the test object A is considerably different from the refractive index of air, and the test wave b transmitted through the test object A is as long as the incident surface and the exit surface of the test object are not parallel. Converges and diverges irregularly. On the other hand, to image interference fringes with an interferometer,
The test wave b must be a substantially parallel light beam. Therefore, the following configuration is adopted because the test wave b transmitted through the test object A becomes almost parallel light beam regardless of the shape of the test object A.

That is, the test object A is installed in a container-like cell 27 provided in the optical path of the test wave b. The cell 27 is filled with a test solution B whose refractive index is almost the same as the refractive index of the test object A. The specimen A
Is mounted on a turntable 29, and the turntable 29 is rotatable by an arbitrary angle around a rotation axis O orthogonal to the test wave b by a servo motor (not shown) or the like. Both ends of the cell 27, that is, the entrance window 31 and the exit window 33 of the test wave b are parallel to each other, and optical flats 35 and 37 having high surface accuracy are attached to each of them to shield in a liquid-tight manner. Therefore, the cell 27 filled with the test object A and the test solution B becomes an object having a uniform refractive index as a whole,
In addition, since the incident surface and the emission surface are parallel, the test wave b transmitted through the cell 27 is emitted as a substantially parallel light flux.

The interference fringe image is detected by the interference fringe detector 15, photoelectrically converted into an electric image signal, A / D converted, and input to the arithmetic unit 17. The arithmetic unit 17 includes a transmitted wavefront measuring unit 18 that performs a measurement operation of a transmitted wavefront by analyzing an interference fringe image by a phase shift method or the like.

Next, a method for measuring the refractive index of the test object A using the measuring apparatus having the above-described configuration will be described with reference to the flowchart of FIG. First, the test object A is moved to the turntable 29.
In the state in which the interference fringe image is not set in the initial state, the image signal of the interference fringe image output from the interference fringe detector 15 is taken into the arithmetic processing unit 17, and the transmitted wavefront measuring unit 18 inside the arithmetic processing unit analyzes the interference fringe image. Measure the transmitted wavefront. Based on the measurement result, an initial process for eliminating a steady error component of the measurement device itself is performed.

Next, the test object A is set on the turntable 29 (S11), and the turntable 29 forms an interference fringe on the imaging surface of the interference fringe detector 15 at the position of θ = 0 (reference position). An image signal of the interference fringe image output from the interference fringe detector 15 is taken into the arithmetic processing unit 17 to analyze the interference fringe image (S1).
2).

In the measurement of the transmitted wavefront when the turntable 29 is at the initial rotation position, the analysis results of the interference fringe image are integrated in the thickness direction (the optical axis direction) of the test object A, and this alone results in uneven refractive index. The spatial position of a part cannot be specified.

Then, the turntable 29 is moved from the initial rotation position to
As shown by the arrow, the test object A on the turntable 29 is rotated with respect to the optical axis of the test wave b by rotating it by a predetermined angle (S1).
3). Thus, even if the test object A is rotated and displaced, the interference fringe image is formed on the imaging surface of the interference fringe detector 15. In this state, the image signal of the interference fringe image output from the interference fringe detector 15 is taken into the arithmetic processing unit 17 and the transmitted wavefront is measured (S1).
2). Thus, for example, interference fringes are formed a plurality of times from the direction of 180 ° (π) or 360 ° (2π) in 1 ° increments (S14), and the transmitted wavefront is measured, and the computer, that is, the arithmetic processing unit Re-synthesize on 17. The reconstruction of this image can be performed by using a well-known X-ray CT (Computed T
(omography) analysis method.

FIG. 6 shows the principle of the CT method, in which the transmitted wavefront data p by the test wave incident from an angle θ is shown.
If (x, θ) is one-dimensionally Fourier-transformed with respect to the variable x, the θ-direction component in the polar coordinate expression of the two-dimensional Fourier transform of the refractive index distribution Δn (x, y) to be obtained can be obtained.

That is, the transmitted wavefront is measured over an angle range of 0 ≦ θ ≦ 2π or 0 ≦ θ ≦ π, and the transmitted wavefront data is connected by phase connection processing (S15), and one-dimensional Fourier transform is performed (S16). According to the projection cut plane theorem, the result of the Radon transform of an object having a physical distribution amount, that is, the result of one-dimensional Fourier transform of projection data from the direction of the angle θ is the θ-direction component in the polar coordinate expression of the two-dimensional Fourier transform of the object Matches. Therefore, the Fourier-transformed polar coordinate data P (x, θ) of each section is converted into orthogonal coordinate data (S17), and then two-dimensional inverse Fourier transform is performed (S17).
18) Further, by converting the refractive index into the refractive index, the three-dimensional refractive index distribution of the test object A can be reconstructed.

[0019]

However, according to the above-described method for measuring the refractive index distribution, each time the test object is rotated, the electric-displacement conversion element 19 is driven to change the reference wave a and the test wave b. It is necessary to adjust the optical path length to have a phase difference of nπ / 2, and it takes a long time for the measurement.

The present invention has been made in view of such circumstances, and an object of the present invention is to provide a measuring method and an apparatus capable of measuring a phase distribution of a test object in a short time.

[0021]

In order to achieve the above object, the present invention divides coherent light from the same light source into a reference wave serving as a reference and a test wave passing through an object to be referred to. The wave and the test wave are overlapped to form interference fringes, the test object is immersed in a test solution having a refractive index substantially the same as that of the test object, and the test object is rotated around an axis orthogonal to the optical axis, and each rotation is performed. In the method of measuring the interference fringe intensity at the position, analyzing the interference fringe intensity, calculating the transmitted wavefront, and measuring the phase distribution of the test object from the transmitted wavefront, the optical path difference between the reference wave and the test wave Is characterized in that the measurement is always kept constant.

The reference wave and the test wave are tilted at a predetermined angle, the analysis of the interference fringe intensity is performed by the Fourier transform method, and the test object is rotated one after another while rotating around an axis orthogonal to the optical axis. The transmitted wavefront is measured and CT (comput
(Ed tomography) method, and the phase distribution of the test object can be measured three-dimensionally.

The measuring apparatus of the present invention divides coherent light from the same light source into a reference wave serving as a reference and a test wave passing through a test object, and superimposes the reference wave and the test wave to form an interference fringe. Forming
The specimen is immersed in a test solution having a refractive index substantially the same as that of the specimen,
The test object is rotated around an axis perpendicular to the optical axis to measure the interference fringe intensity at each rotational position, analyze the interference fringe intensity, calculate the transmitted wavefront, and calculate the phase of the test object from the transmitted wavefront. In an apparatus for measuring distribution, a fixed mirror is provided in the optical path of the reference wave and / or the test wave, at least one of the mirrors is tiltable, and the reference wave and the test wave cross at a predetermined angle. It is characterized by:

[0024]

Embodiments of the present invention will be described below in detail with reference to the drawings. The phase distribution measuring apparatus of the present invention, similarly to a conventional measuring apparatus, holds a test object A in a sample solution B having a refractive index substantially the same as the test object A, measures a transmitted wavefront, and (Including a refractive index distribution and a concentration distribution).

FIG. 1 shows a measuring apparatus according to the present invention, which is substantially the same as the conventional example, except that there is no electric-displacement conversion element 19 and the reflection mirror 7 is fixed. The reflection mirror 7 is tilted by γ from a normal position, that is, a position at 45 ° with respect to the incident light.

In the present invention, a Fourier transform method is used as a method for analyzing interference fringes, instead of the conventional phase shift method. The phase shift method is a temporal modulation, whereas the Fourier transform method is a spatial modulation, so that it is suitable for the high-speed measurement targeted by the present invention.

In the measuring apparatus of FIG. 1, first, the inclination angle γ of the reflection mirror 7 is determined as follows. Reflection mirror 7
Is set to the position of γ = 0, and the interference fringes are in a null state. When only a slight angle γ is tilted from this position, vertical stripes are formed. This is the interference fringe having the spatial carrier frequency f ₀ .

Next, the test object A is set and interference fringes are formed in the same manner. From this interference fringe, the transmitted wavefront is measured as follows in accordance with the flowchart of FIG. First, the intensity distribution of the interference fringes is

(Equation 1)

Is given by ψ (x) represents the transmitted wavefront aberration of the test object, and a (x) and b (x) represent the light amount unevenness.
By transforming equation (1),

(Equation 2) Where c ^* is a complex conjugate and

(Equation 3) It is. When the Fourier transform is performed (S1),

(Equation 4)

(Equation 5)

Here, A (f) and C (f) are Fourier transforms of a (x) and c (x), respectively. a (x),
When c (x) is sufficiently slower than f ₀ , the three spectra are completely separated as shown in FIG. 2A (S2).

Therefore, only the spectrum C (f−f ₀ ) of the second term is extracted by filtering, and as shown in FIG. 2B, the spectrum is shifted to the origin by f ₀ (S3), and the inverse Fourier transform is performed. (S4). Here, taking the complex logarithm,

(Equation 6) By taking the imaginary term, it is completely separated from the unnecessary signal b (x). Therefore, the phase angle of c (x)

Equation 7 (S6), ψ (x) becomes a (x),
b (x) is obtained independently.

Next, according to the flowchart of FIG.
A method of reconstructing a refractive index distribution (phase distribution) by a computed tomography (T) method will be described. The CT analysis method includes a successive approximation method and a filtered back projection method, and the Fourier transform method is known as a simplest and strict method for reconstructing an image from projection data. The algorithm of the Fourier transform used here is different from that of the Fourier transform used for the analysis of the interference fringes. Although easily misleading, both are used as publicly known, so the names are intentionally given the same name.

The test object A is rotated over the range of 0 ≦ θ ≦ π, and each transmitted wavefront is measured as described above according to the flowchart of FIG. Thereafter, the process is performed in accordance with S15 and subsequent steps in the flowchart of FIG. 5, and the phase distribution can be obtained.

In the above embodiment, the reflection mirror 7 has an angle γ
However, the reflection mirror 9 may be tilted at an angle γ to tilt the test wave b. Further, it is also possible to adopt a configuration in which both the reflection mirrors 7 and 9 are tilted. In any case, according to the above embodiment, it is not necessary to provide a movable part such as a piezo element in the interference optical system, and the rigidity of the optical system is high, the reliability is high, and a simple measuring device can be obtained. it can.

In the conventional phase shift method, the optical path difference must be modulated to measure one transmitted wavefront, and the interference fringe intensity signal must be captured four or five times. In contrast to the necessity of repeatedly performing the rotation operation, the Fourier transform method of the present invention can perform the operation only once, so that the interference fringe measurement can be performed dynamically while rotating, and the refractive index can be measured in a very short time. It is possible to measure the distribution. This effect is effective not only for shortening the measurement time but also for an object whose test object changes with time.

[0036]

According to the present invention as described above,
The coherent light from the same light source is divided into a reference wave serving as a reference and a test wave passing through the test object, and the reference wave and the test wave are overlapped to form an interference fringe, and the test object has a refractive index. Is immersed in the same sample solution as the test object, rotates the test object around the axis perpendicular to the optical axis, measures the interference fringe intensity at each rotation position, analyzes the interference fringe intensity, and calculates the transmitted wavefront In the method of measuring the phase distribution of the test object from the transmitted wavefront, since the measurement is performed while keeping the optical path difference between the reference wave and the test wave constant, a movable portion such as a piezo element is provided in the interference optical system. This eliminates the need for a simple measuring device with high rigidity and high reliability of the optical system.

If the reference wave and the test wave are tilted at a predetermined angle and the interference fringe intensity is analyzed by the Fourier transform method, the measurement can be performed at a higher speed than the phase shift method.

The transmitted wavefront is measured one after another while rotating the test object around an axis orthogonal to the optical axis, and the CT (computed) is measured.
By performing reconstruction using a tomography method and three-dimensionally measuring the phase distribution of the test object, it is possible to measure the phase distribution of the entire test object at high speed.

[Brief description of the drawings]

FIG. 1 is a plan view showing a configuration of a phase distribution measuring device of the present invention.

FIG. 2 is a diagram showing a state where a spectrum is extracted from a transmitted wavefront by the method of the present invention.

FIG. 3 is a flowchart for measuring a transmitted wavefront by the method of the present invention.

FIG. 4 is a plan view showing a configuration of a conventional phase distribution measuring device.

FIG. 5 is a flowchart showing a procedure for obtaining a phase distribution from measurement of interference fringes.

FIG. 6 is a diagram illustrating the principle of CT analysis.

[Explanation of symbols]

 A test object B reagent O rotation axis 1 light source

Claims (5)

[Claims] An interference fringe is formed by dividing coherent light from the same light source into a reference wave serving as a reference and a test wave passing through a test object, and superimposing the reference wave and the test wave to form interference fringes. The specimen is immersed in a sample solution with a refractive index almost the same as the specimen, the specimen is rotated around an axis perpendicular to the optical axis, the interference fringe intensity is measured at each rotation position, and the interference fringe intensity is analyzed. Calculating the transmitted wavefront by using the transmitted wavefront, and measuring the phase distribution of the test object from the transmitted wavefront, wherein the measurement is performed while keeping the optical path difference between the reference wave and the test wave constant. . 2. The phase distribution measuring method according to claim 1, wherein the reference wave and the test wave are tilted at a predetermined angle. 3. The phase distribution measuring method according to claim 1, wherein the analysis of the interference fringe intensity is performed by a Fourier transform method. 4. The transmitted wavefront is measured one after another while rotating the test object around an axis orthogonal to the optical axis, and the CT (compute) is measured.
The phase distribution measuring method according to any one of claims 1 to 3, wherein the phase distribution of the test object is three-dimensionally measured by performing reconstruction using an ed tomography method. 5. A coherent light beam from the same light source is divided into a reference wave serving as a reference and a test wave passing through a test object, and the reference wave and the test wave are overlapped to form an interference fringe. The specimen is immersed in a sample solution with a refractive index almost the same as the specimen, the specimen is rotated around an axis perpendicular to the optical axis, the interference fringe intensity is measured at each rotation position, and the interference fringe intensity is analyzed. In the apparatus for calculating the transmitted wavefront and measuring the phase distribution of the test object from the transmitted wavefront, a fixed mirror is provided in the optical path of the reference wave and / or the test wave, and at least one of the mirrors can be tilted. ,
An apparatus for measuring a phase distribution, wherein a reference wave and a test wave cross at a predetermined angle.